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Topic: Wm mis-explains what he means by a Binary Tree
Replies: 8   Last Post: Feb 7, 2014 2:54 PM

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Posts: 8,833
Registered: 1/6/11
Re: WM mis-explains what he means by a Binary Tree
Posted: Feb 6, 2014 4:19 AM
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In article <>,
WM <> wrote:
> Am Donnerstag, 6. Februar 2014 00:19:51 UTC+1 schrieb Ben Bacarisse:
> > The properties of a path defined by a
> > supposed bijection can be argued about perfectly well.

> If the path can be named.

WM has this thing about having to name everything. Nut he's SOL because
in real mathematics there are more things than names.
For example. In a Complete Infinite Binary Tree ther are more paths than
WM can find names for them.

> > What exactly is the "contrary"?
> The contrary is that Cantor's argument exclusively is based upon digits at
> finite positions.

On the contrary, Cantor's argument was not about digits at all but about
infinite strings of the letters 'm' and 'w'.

> A rational-complete list covers all these positions.

Claimed but not proved
and not provable anywhere outside of WMytheology,

> And
> there are no digits at infinite positions

But there can be digits at infinitely many different finite postions,
which scuttles WM's arguments entirely.

> > > That's what we call an antinomy. It is a well-known paradox
> > >that matheologians cannot see the other side.

> > Well it would be a problem except that the contrary is not true.

> But it is true. A rationals-complete list contains all digit sequences that
> can be subject to the diagonal argument

The finitely defined real number r = Sum_(n in |N) 1/2^(n!), in base 2,
is not anywhere in WM's "rationals-complete list" or in his
pseudo-binary tree, but does represent a path in any Complete Infinite
Binary Tree outside of WMytheology. .

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